To solve the division problem [tex]\(-\frac{0.166}{0.030}\)[/tex], we need to follow specific steps and pay close attention to significant digits. Here's a step-by-step guide:
1. Identify the Numbers and Their Significant Digits:
- The numerator is [tex]\( -0.166 \)[/tex]. This number has 3 significant digits: 1, 6, and 6.
- The denominator is [tex]\( 0.030 \)[/tex]. This number also has 3 significant digits: 3, 0, and another 0.
2. Perform the Division:
- When we divide, we get:
[tex]\[
-\frac{0.166}{0.030} = -5.5333333333\ldots
\][/tex]
3. Determine the Significant Digits for the Result:
- According to the rules for multiplication and division, the result should be expressed using the same number of significant digits as the factor with the fewest significant digits.
- In this case, both the numerator and denominator have 3 significant digits. Hence, our final answer should have 3 significant digits.
4. Round the Result:
- We need to round [tex]\(-5.5333333333\ldots\)[/tex] to 3 significant digits.
- Looking at the digits, the number [tex]\( -5.5333333333\ldots \)[/tex] rounds to [tex]\( -5.53 \)[/tex] when considering just 3 significant digits.
5. Final Answer:
- The result of the division [tex]\( -\frac{0.166}{0.030} \)[/tex] to the correct number of significant digits is:
[tex]\[
-5.53
\][/tex]
- Therefore, the answer is negative (-).
